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8. Sequences and Series
medium
$0.5737373...... = $
A
$\frac{{284}}{{497}}$
B
$\frac{{283}}{{495}}$
C
$\frac{{568}}{{990}}$
D
$\frac{{567}}{{990}}$
Solution
(c) Given series $0.5737373……$
$= 0.5 + 0.073 + 0.00073$
$= 0.5 +$ $\frac{{73}}{{1000}} + \frac{{73}}{{100000}} + ….$
= $0.5 + 73\left[ {\frac{1}{{1000}} + \frac{1}{{100000}} + …..} \right]$
= $0.5 + 73\left[ {\frac{{1/1000}}{{1 – \frac{1}{{100}}}}} \right]$
= $0.5 + \frac{{73}}{{1000}}.\frac{{100}}{{99}} = \frac{5}{{10}} + \frac{{73}}{{990}}$
= $\frac{{495 + 73}}{{990}} = \frac{{568}}{{990}}$.
Standard 11
Mathematics
